That's not entirely true. In the early part of the new century the Sox had a number of guys...Thomas, Ordonez, Lee, Konerko who'd all bash 25-40 home runs and hit between .270 and .320.

The problem is though hitters like that are scarce. To be able to get three, four, five of them in the same lineup at the same time takes some luck and probably a payroll today far beyond the Sox means.

Lip

Look at those names and you'll find your real answer. It's not payroll, it's organization. Three of those players came up in the Sox organization. The fourth was a trade for a player of a similar background (1 or 2 years in the majors, one off year).
Has the Sox organization produced any hitters like that since then?